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Weber’s Law in Behavioral Economics

In the mid-19th century Ernst Weber, one of the founders of psychology, was interested in these sorts of range effects. One of his most famous experiments was also one of his most simple.

Weber’s Law

Weber brought people into his laboratory and then had them lift one object and then another and then he asked them to guess whether one was heavier. He found that the difference in weight needed to guess correctly was a constant proportion of the weight.

For example: people could reliably distinguish a 2 pound weight from a 2 pound 1 oz. weight but they couldn’t tell the difference between a 20 pound weight and a 20 lbs. and 1 oz. weight. At that larger range the difference would need to be about 1/2 pound or so to be noticeable.

When lifting two objects people can tell which one is heavier if they differ by about 2 or 3% in weight this phenomenon has come to be known as Weber’s law. The difference needed to discriminate to stimulate what psychologists call a just noticeable difference is a constant proportion of their magnitude.

You’ve probably experienced this yourself: if you were in the market for a new laptop computer you may have lifted two different models and notice that one was heavier than the other.

That difference in weight was probably only a few ounces or maybe a pound but it still seemed very meaningful, but if you lifted two chairs a differed and weighed by only a few ounces, you’d never be able to tell them apart.

Weber’s law seems to be practically universal. It holds for the weight of things we lift the brightness of things we see the loudness of things we hear and even for our ability to represent numerical quantities.

Small differences matter

There is a correspondingly larger range of potential values that makes our judgments much less precise. We don’t notice small differences against that backdrop. Once our range expands differences need to be much larger to matter for our decisions.

But why are these range effects so ubiquitous? To understand why let’s dig a little bit deeper into our biology. Our brains face the challenge of dealing both with very small quantities and with very large quantities.

Visual perception has to work for dark starlight and for bright sunlight and decision-making has to work for cups of coffee and for sports cars. So how do our brains represent things both small and large?

Our brain adapts from processing small quantities to processing big quantities by changing the scale. That has a cost when we move from small to big we lose precision. A dollar seems meaningful for a cup of coffee but it doesn’t matter for a television. That’s the essence of arrange effect.

Implications of range effects

Implications of range effectsI want to highlight two such implications: one is straightforward and the other is more subtle. First let’s quickly revisit the definition of a range affect: “a meaningful difference in some quantity is inversely proportional to its range”.

Differences become less meaningful as quantities get bigger. Now that sounds a lot like the idea of diminishing marginal utility for money.

This idea which is a bedrock concept in economics was first articulated in the 18th century by Daniel Bernoulli who said “the utility resulting from any small increase in wealth will be inversely proportionate the quantity of goods previously possessed”.

So, diminishing marginal utility for money is a straightforward consequence of a much deeper phenomenon. Small differences don’t see meaningful when dealing with large amounts.

There’s a second implication of range effects though, one that helps us understand a particularly thorny problem for behavioral economics. Suppose that someone offers you a coin flip gamble: heads I give you $11 tales you give me $10.

Some people will accept this offer, but most won’t. Most people turn down gambles like this unless the potential gain is twice as big or bigger the potential loss.

let’s think about what this implies though for the rate of diminishing marginal utility for money. The economist Matthew Raben noted that if you turn down that gamble it implies that the utility for the 11th dollar above your current well state is considerably less than that of the 10th dollar below your current well state. How much less?

10÷11 or about 90%, or stated another way turning down this gamble implies that the value of the dollar diminishes by 10% over a range of $21. This rate of diminishing marginal utility is a problem.

That implies that the value of money diminishes faster when we are dealing small amounts but the coin flip gambles but much much more slowly when were dealing with large amounts like our retirements.

That’s the basic idea of a range effect: our sense of a meaningful difference in some quantity is inversely proportional to its range.

Avoiding range effects

We can take steps to avoid range effects or at least to minimize her unwanted influence on her decisions. Let me offer three specific recommendations. First begin with small decisions.

If you begin with the decision involving large amounts of money like whether to buy a car then you may lose the ability to make good decisions about smaller amounts of money, say whether to purchase upgraded floor-mat for the car.

$100 might not seem that important after you decided to spend tens of thousands of dollars, but it’s still your money.  By beginning with smaller decisions and moving up to bigger decisions later you’ll avoid losing perspective on small but still important decisions.

Second avoid undesirable options that exaggerate range effects. Suppose that you live in a large city and are looking for an apartment. You first tour 1000 square-foot apartment that’s in the middle of your price range venue tour and 1100 square-foot apartment it’s larger but somewhat more expensive, then on a whim you tore a much larger 2000 square-foot apartment, when the you know in advance that you won’t by because it’s located too far away from your place of work.

That last option is undesirable because of its location, so in principle it shouldn’t affect your decision between the other two options, but it might. Touring that much larger apartment increases the range of apartment sizes that you’ve seen, so the difference in size between the other two apartments will seem less meaningful.

The same principle holds for other factors too: considering in a very high-priced option will make differences in price seem less important. Marketers know this and they ensure that their high priced alternatives in many decisions even if they don’t expect customers to choose them.

Finally force yourself to recalibrate. Don’t lose perspective when making what seem like big decisions. For many of us the largest decisions we make involve purchases of cars and houses for which the different options might vary by thousands or tens of thousands or hundreds of thousands of dollars. If you just consider those options in isolation, it’s easy to be caught up in range effects.

So don’t think about the seemingly big decisions in isolation suppose if two cars differ price by $5000. Force yourself to think about how else you can use that money could it go for a vacation, membership at a gym, recurring bills or all the above.

By thinking about the smaller decisions to you regain some perspective. Perhaps the higher price option really is worth it to you or perhaps you’d rather take the lower-priced option and have opportunities for many small rewards as well.

As a final thought, I’d like to emphasize that range effects are good for us
it’s really quite remarkable their decision-making is so adaptive and flexible
we can deal both with the innumerable small decisions throughout each day and with the rare larger decisions that shape the course of our lives for years to come.